During the current quenching after a major disruption, part of the stored magnetic energy is dissipated in the centre of a post-disruptive plasma. This period has been experimentally investigated in the TFR tokamak. The plasma resistance is found to be in agreement, within a factor of three, with its value expected from Spitzer's law. The energy balance is dominated by conduction and convection in the core of the plasma and by charge exchange and radiation at the edge. The most probable mechanism to be invoked for any explanation of the high heat conductivity (107 cm2·s−1) is parallel transport along ergodic field lines. Consequences for the scaling law governing the current decrease rate are discussed.